At what energy does gravity unite with grand unified theories in the early universe?

Unification of gravity with GUTs is usually expected at the Planck energyE _pl10¹⁹ GeV. However, the vastly different values of the two couplings atE _Pl ( _GUT 1, _grav 1) would make such unity (atE _Pl) implausible unless there is a drastic change in the behavior of either gravity or GUTs aroundE _Pl. We picture gravity and GUTs to be unified at energies >E_Pl with a single dimensionless coupling constant ( _U 1) and described by a scale-invariant action quadratic in the Weyl curvature (with Yang-Mills fields). Breaking of scale invariance atE _Pl then separates the interactions into gravity, now described by a Hilbert action with a dimensionalG and GUTs woth a dimensionless _GUT and YM action. Problems with Klein-Kaluza unification of gravity with GUTs are also discussed in this context.     

Equilibrium polymerization in a solvent: Solution on the Bethe lattice

The lattice model for equilibrium polymerization in a solvent proposed by Wheeler and Pfeuty is solved exactly on a Bethe lattice (core of a Caylay tree) with general coordination numberq. Earlier mean-field results are reobtained in the limitq, but the phase diagrams show deviations from them for finiteq. Whenq=2, our results turn into the solution of the one-dimensional problem. Although the model is solved directly, without the use of the correspondence between the equilibrium polymerization model and the diluten0 model, we verified that the latter model may also be solved on the Bethe lattice, its solution being identical to the direct solution in all parameter space. As observed in earlier studies of the puren0 vector model, the free energy is not always convex. We obtain the region of negative susceptibility for our solution and compare this result with mean field and renormalization group (-expansion) calculations.     

Level structure of 68 149 Er81 and high-spin isomerism in proton-richN=81, 82, 83 nuclei

The level structure of theN=81 nucleus¹⁴⁹Er has been studied by γ-ray spectroscopy following the reaction⁹²Mo+255 MeV⁶⁰Ni. Yrast levels in¹⁴⁹Er are established up to ~3.3 MeV, including 0.61 and 4.8 μs isomeric states. Most of the observed levels are interpreted as seniority-three states arising from the coupling of s_1/2, d_3/2 and h_11/2 neutron holes with πh ₁₁ ^2/n . Isomers identified in the reaction⁹⁶Ru+255 MeV⁵⁸Ni are tentatively assigned to¹⁵¹Yb. TheB (E2) values of high-spin isomers inZ=66?70,N=81?83 nuclei are surveyed.     

Vibrational modes and infrared absorption of interstitial oxygen in silicon

A quasi-linear Si₂O molecule model (QLMM) is suggested from an analysis of the configuration and the interactions of an isolated oxygen atom with its neighbor silicon atoms. The vibrational modes are assigned and the infrared absorption spectra are calculated in detail with the model. The theoretical results are in reasonably good agreement with reported experimental values. This agreement shows that for the analysis of the vibrational modes of the interstitial oxygen atom in silicon crystals it is not necessary to consider the coupling of the molecule with the rest of the lattice. The interaction of the oxygen atom with its six second-nearest silicon atoms only causes the level separation of the ₂ mode and the formation of the fine structure.     

g-Factor of the first 2+ state in theN=82 nucleus138Ba

The 2 ₁ ⁺ level of¹³⁸Ba has been Coulomb excited with a 105 MeV³²S beam. The precession of the gamma ray angular distribution induced by the transient magnetic field when traversing a 2.14 mg/cm² iron foil, has been measured to be 15.6(1.7) mr. A value of g(¹³⁸Ba 2 ₁ ⁺ )=0.72(11) was obtained assuming for the transient field strength the Chalk River calibration. The field parametrization has been checked using the first 2⁺ state in¹⁵⁰Sm as probe. Theg value obtained is sensibly lower than predicted by large scale shell model calculations in a proton subspace. Theg-factor of the first 2⁺ state in¹⁴⁸Sm has been remeasured yieldingg(¹⁴⁸Sm 2 ₁ ⁺ )=0.246(22).     

Parity violation in the 17/2−–17/2+ doublet in93Tc

The parity-violating mixing of the 17/2^– and 17/2⁺ levels in⁹³Tc nuclei, polarized by the tilted multifoil interaction, was measured by the observation of the forward-backward-ray asymmetry. The nuclear polarization, induced by the tilted multifoils, was measured directly for the neighboring^88,90Zr isomers. The forward to backward asymmetry was determined to be A=(2.5±2.1) 10^–3 which implies a parity violating matrix element ¦H _PV )¦=(4.0±3.7)meV.     

Lattice instability in Hf1-x Ta x V2 compounds

The temperature dependence of the electric quadrupole interaction frequency _l ^o , experienced by the¹⁸¹Ta probe occupying Hf site in the compounds Hf_1-xTa_xV₂ has been measured for x=0.06, 0.10 and 0.20 in the temperature region between 8.5 K to 296 K. The measurements show lattice transformation in all the three compounds below 120 K.     

Fast proton conductivity of polycrystalline titanoniobates

The proton conductivity of three layer-type compounds was studied: H₃OTi₂NbO₇. H₂O, HTiNbO₅ and HTiTaO₅. Measurements were made between 20 °C and 90°C on pellets pressed from crystalline powders and soaked with pure water. The hydrated compound had the highest conductivity, (20°C)-6.3–6.9·10^–4 (cm)^–1. Acid ions from the exchange process were quite firmly retained in its layer structure and contributed significantly to the measured conductivity. Consistent results were obtained after prolonged washing with water.Dedicated to Professor Harry Thomas on the occasion of his 60th birthday     

Interaction of an ultrasonic wave with a bubbly mixture

The interaction of an ultrasonic wave with a bubbly two-phase flow is studied both experimentally and theoretically. Brief theoretical reviews of acoustic wave generation by a piston and of the interaction of a plane wave with a single bubble are given. A theory relating ultrasonic wave transmission through a bubbly flow with two-phase flow parameters, notably the bubble size and the volumetric interfacial area, is derived and compared with preliminary data. The theoretical and experimental limitations concerning the application of ultrasonic transmission measurements to the study of bubbly flow are discussed in detail, and recommendations for future work in this area are made.Nomenclature A projected cross-sectional area of a bubble - a bubble radius - a _T emitter radius - c speed of sound - d equivalent bubble diameter - I intensity - I ₀ incident intensity - J ₀ Bessel function of zero order - J ₀ Bessel function of first order - j ₁ spherical Bessel function of the first kind and of order l - k wave number - n _l spherical Bessel function of the second kind (Nishi's notation) - n number of bubbles per unit volume or per unit area - P ₀ pressure amplitude at the emitter; equilibrium pressure in the liquid - p pressure perturbation - r spherical coordinate, radial distance to the x-axis - S total scattering cross-sectional area, surface of the piston - S _i scattering cross-sectional area of the i-th bubble - T transmittance - t time - U complex source strength divided by the source area - W ratio of radial distance from the axis on the emitter surface to the radius of the emitter - x axis coinciding with the direction of propagation of the plane wave; distance between the transducers - void fraction - interfacial area per unit volume - spherical coordinate - ultrasonic wavelength - density - angular frequency